Experimental Densities of Hexane+ Benzothiophene Mixtures from

J. Chem. Eng. Data 2007, 52, 2455-2461

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Experimental Densities of Hexane + Benzothiophene Mixtures from (313 to 363) K and up to 20 MPa Luis E. Camacho-Camacho and Luis A. Galicia-Luna* Laboratorio de Termodina´mica, ESIQIE, Instituto Politećnico Nacional, UPALM, Edif. Z, Secc. 6, 1ER piso, Lindavista, C. P.: 07738, Me´xico, D. F., Mexico

Experimental densities of hexane and hexane + benzothiophene mixtures were obtained via a vibrating tube densimeter. Densities of hexane were measured from (313 to 363) K and pressures up to 25 MPa. For the case of hexane (1) + benzothiophene (2) mixtures, the experiments were performed at five compositions (x1 ) 0.0629, 0.2588, 0.4495, 0.7491, and 0.9432) in the same range of temperatures at pressures up to 20 MPa. Uncertainties for measured densities were estimated within 0.2 kg‚m-3. The obtained densities of hexane were compared with those values reported in the literature and with the results obtained by the Tait equation and the equation of state proposed by R. Span and W. Wagner (Int. J. Thermophys. 2003, 24, 1-39). These were also correlated with a modified five-parameter Toscani-Szwarc equation (MTS). Good agreement was found in all cases. Excess molar volumes for the mixtures, as well as isothermal compressibilities and isobaric thermal expansivities of hexane, were calculated using the reported parameters for the MTS equation.

Introduction Sulfur content in fuels is regulated by international norms due to the contamination and acid rain they produce in the atmosphere. A possible way to eliminate the contamination is by extracting these compounds from fuels, particularly gasoline and diesel. For the design of this kind of process, basic information for the thermodynamical properties, such as phase equilibria, solubilities of sulfur compounds in some solvents, densities of liquid mixtures, etc., is required. However, scarce information concerning the properties for sulfur compounds or its mixtures is available in the literature. Previous works to study the behavior of sulfur and aromatic compounds in supercritical CO2 and in mixtures of CO2 + cosolvents have been presented from our workgroup.1-6 In this work, densities of mixtures of a sulfur compound and an alkane are used as basic information to simulate a fuel. Gasoline has compounds more important than hexane; however, this alkane was selected in this work as a first attempt to represent a fuel added to benzothiophene which was the model sulfur compound. Alkanes with a greater number of carbons will be tested in future works. Hexane has been used mainly as a solvent in many applications such as, for instance, liquid-liquid extractions of seed oils, solvent in adhesives, and leather tanning. This alkane is a very important solvent in industry and research. Properties of hexane previously reported in the literature include measurements of densities and speeds of sound, calculations of isothermal compressibilities and isobaric thermal expansivities, and correlations of data.7-9 On the other hand, experimental data for benzothiophene are scarce, and it is necessary to know its phase behavior in contact with alkanes for future extractions. This work reports the experimental densities of hexane and five mixtures of hexane + benzothiophene, at temperatures from (313 to 363) K and pressures up to 25 MPa for hexane and 20 MPa for the mixtures. Densities of hexane were correlated with the modified five-parameter Toscani-Szwarc (MTS) equation,6 and their optimal parameters were used to calculate densities * To whom correspondence should be addressed. E-mail: [email protected]. Tel.: (52) 55 5729-6000, Ext. 55133. Fax: (52) 55 5586-2728.

and derivative properties, such as isothermal compressibilities and isobaric thermal expansivities. Excess molar volumes for hexane + benzothiophene mixtures were calculated by using reported densities and the five-parameter MTS equation6 for the densities of pure compounds. The data for these mixtures have not been previously reported in the literature.

Experimental Section Materials. Hexane (> 99.5 %) was supplied by Fluka (Germany); benzothiophene (99.0 %) and water (99.995 %) were obtained from Sigma-Aldrich (USA); and Air Products-Infra (Mexico) supplied the nitrogen (> 99.998 mol %). Liquid compounds were used without any further purification, except for careful degassing under vacuum before the measurements. Nitrogen was used as received. Apparatus. The experimental apparatus has been previously described by Zuń˜iga-Moreno et al.4-6 It is based on the staticsynthetic method, with a sapphire tube feeding cell coupled to a vibrating tube densimeter (VTD). The 10 cm3 sapphire cell is placed inside an air bath. The temperature is maintained within ( 0.03 K and is monitored with a platinum probe (Specitec, model Pt100). The Pt100 probe is inserted at the top of the cell and connected to a digital indicator (Automatic Systems Laboratories, model F250). All the platinum probes used in this work were calibrated with a 25-Ω reference probe (Rosemount, model 162CE, uncertainty 0.005 K) coupled to a calibration system (Automatic Systems Laboratories, model F300S). The pressure inside the measuring cell was registered by means of a pressure transducer (SEDEME, model 250) coupled to a digital multimeter (Hewlett-Packard, model 34401A). The transducer was calibrated against a dead weight balance (Desgranges & Huot, model 5304 Class S2, uncertainty 0.005 %). The total uncertainty was estimated to be within 0.008 MPa. The mixture in the homogeneous phase is stirred inside the cell with the help of a magnetic rod and fed to the vibrating tube densimeter (Anton Paar, model DMA 512) made of Hastelloy C-276. The temperature of the VTD measured with a Pt100 probe is maintained within ( 0.03 K by means of a liquid bath (Polyscience, model 9510). The VTD was calibrated

10.1021/je7003929 CCC: $37.00 © 2007 American Chemical Society Published on Web 10/13/2007

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Journal of Chemical and Engineering Data, Vol. 52, No. 6, 2007

Table 1. Experimental Densities G of Hexane T/K ) 313.12

T/K ) 323.05

T/K ) 332.85

T/K ) 342.73

T/K ) 352.56

T/K ) 362.40

p/MPa

F/kg‚m-3

p/MPa

F/kg‚m-3

p/MPa

F/kg‚m-3

p/MPa

F/kg‚m-3

p/MPa

F/kg‚m-3

p/MPa

F/kg‚m-3

1.019 1.010 2.044 3.023 4.018 5.016 6.012 7.016 8.016 9.020 10.018 11.020 12.004 13.007 14.015 15.006 16.023 17.015 18.011 19.009 20.016 20.995 22.018 23.018 24.013 25.002

642.2 613.9 643.5 644.6 645.8 647.0 648.1 649.2 650.3 651.4 652.5 653.5 654.6 655.6 656.6 657.6 658.6 659.6 660.5 661.4 662.4 663.3 664.2 665.1 666.0 666.8

1.030 1.017 2.010 3.021 4.018 5.014 6.007 7.010 8.012 9.020 10.008 11.021 12.011 13.007 14.007 15.035 16.011 17.021 18.020 19.013 20.001 21.028 22.004 23.010 24.021 25.018

633.0 604.0 634.3 635.6 636.9 638.1 639.4 640.6 641.8 643.0 644.1 645.2 646.4 647.4 648.5 649.6 650.6 651.6 652.7 653.7 654.6 655.6 656.6 657.5 658.5 659.4

1.020 1.029 2.021 3.022 4.020 5.011 6.016 7.012 8.025 9.012 10.010 11.012 12.019 13.007 14.021 15.014 16.025 17.011 18.035 19.014 20.011 21.015 22.000 23.012 24.022 25.030

623.5 593.8 625.0 626.5 627.8 629.2 630.6 631.9 633.3 634.5 635.7 636.9 638.1 639.2 640.4 641.6 642.8 643.8 644.9 646.0 647.1 648.1 649.1 650.1 651.2 652.2

1.010 2.010 3.011 4.010 5.005 6.031 7.020 8.009 9.015 10.012 11.006 12.014 13.011 14.014 15.008 16.006 17.021 18.016 19.025 20.037 21.025 22.016 23.010 24.023 25.006

613.9 615.5 617.1 618.6 620.0 621.6 623.0 624.4 625.7 627.0 628.4 629.7 630.9 632.2 633.4 634.6 635.7 636.9 638.0 639.2 640.3 641.3 642.5 643.5 644.5

1.017 2.028 3.030 4.024 5.022 6.024 7.027 8.021 9.022 10.020 11.023 12.003 13.021 14.012 15.007 16.016 17.012 18.015 19.003 20.040 21.005 22.035 23.002 24.039 25.000

604.0 605.8 607.6 609.2 610.9 612.5 614.0 615.5 617.0 618.4 619.9 621.2 622.6 623.9 625.2 626.5 627.7 629.0 630.2 631.4 632.5 633.8 634.8 636.0 637.1

1.029 2.020 3.028 4.029 5.040 6.026 7.026 8.004 9.007 10.009 11.009 12.010 13.000 14.028 15.017 16.014 17.004 18.002 18.988 20.027 21.002 22.018 23.013 24.001 25.000

593.8 595.8 597.6 599.5 601.3 602.9 604.7 606.3 607.9 609.4 610.9 612.5 614.0 615.5 616.8 618.1 619.5 620.9 622.1 623.4 624.7 625.9 627.1 628.4 629.5

using water and nitrogen according to the classical method. The density of the mixture is given by10 FF(p,T) ) FH2O(p,T) + [τ2F(p,T) - τH2 2O(p,T)][FH2O(p,T) - FN2(p,T)] τH2 2O(p,T) - τN2 2(p,T)

(1)

where FF(p,T) is the studied fluid density; FH2O(p,T) is the reference density of water; and FN2(p,T) is that for nitrogen. These were calculated using the equations of state of Wagner and Pruss11 and Span et al.,12 respectively; τ(p,T) represents the vibrating period of each fluid. Experimental Procedure. The first step is the sapphire cell loading. The empty cell is degassed and weighted. Then, the cell is again degassed containing a specific amount of benzothiophene. After that, the cell is weighted. The difference between the weight of the empty cell and the cell loaded with benzothiophene is the weight of this compound. Hexane is added to the cell. When a new weighting is performed, the amount of hexane is determined as well as the composition of the mixture. The mass measurements are done with a comparator balance (Sartorius, model MCA 1200), and the uncertainty of the mole fraction is within 1‚10-4. The second step is setting up the experimental conditions. The air and liquid baths are turned on and set up to the lowest temperature of measurement (313 K). The mixture in the sapphire cell is pressurized using nitrogen. This gas enters at the bottom of the cell and pushes up the piston via a pressure generator. The mixture contained in the cell is loaded into the VTD by opening a feeding valve. When the desired temperature is reached and the vibrating period is constant, measurements can be performed. The third step is recording the temperature and vibrating period at each pressure for the studied system. When the maximum pressure is reached, the temperature is changed to 323 K while the pressure is decreased to 1.0 MPa. This step is done for all of the measurement temperatures.

The experimental densities of hexane are presented in Table 1. The obtained densities for the hexane (1) + benzothiophene (2) mixtures measured at five compositions (x1 ) 0.0629, 0.2588, 0.4495, 0.7491, and 0.9432) are reported in Tables 2 to 6. The uncertainty for all measured densities is estimated to be 0.2 kg‚m-3. Modeling. Experimental density data of hexane obtained in this work were correlated using the modified equation of Toscani-Szwarc (MTS) proposed by Zuń˜iga-Moreno et al.6 It is expressed as follows c 1 + c 2p

V)

(2)

c3 - (c4/T + c5/T1/3) + p

where V is the specific volume of the fluid at a specific p and T and ci are the five parameters of the equation. The parameters of eq 2 were optimized by using the MarquardtLevenberg method13 and minimizing the objective function S

∑[(V

S)

exptl i

- Vcalcd )/Vexptl ]2 i i

(3)

i

The statistical values for the correlation were calculated with the following expressions:4,14 absolute average deviation AAD )

1 n

n

∑ |% ∆V |

(4)

i

i)1

mean deviation bias )

1 n

n

∑ (% ∆V )

(5)

i

i)1

standard deviation SDV )

x

1

n-1

n

∑ (% ∆V - bias) i

i)1

2

(6)

Journal of Chemical and Engineering Data, Vol. 52, No. 6, 2007 2457 Table 2. Experimental Densities G of the Hexane (1) + Benzothiophene (2) Mixture at x1 ) 0.0629 T/K ) 313.00

T/K ) 322.95

p/MPa

F/kg‚m-3

1.011 2.027 3.046 4.018 5.014 6.016 7.014 8.008 9.013 10.003 11.005 12.017 13.017 14.023 15.024 16.016 17.014 18.019 19.014 20.000

1112.7 1113.3 1113.9 1114.5 1115.2 1115.7 1116.3 1116.9 1117.6 1118.1 1118.7 1119.3 1119.9 1120.5 1121.0 1121.6 1122.3 1122.8 1123.4 1124.0

p/MPa

F/kg‚m-3

1.028 2.021 3.029 4.021 5.037 6.021 7.021 8.029 9.018 10.003 10.998 12.016 13.012 14.019 15.018 16.018 17.024 18.018 19.024 20.012

1103.4 1104.1 1104.7 1105.4 1106.1 1106.7 1107.4 1108.1 1108.7 1109.3 1109.9 1110.6 1111.2 1111.8 1112.5 1113.1 1113.7 1114.4 1115.0 1115.6

T/K ) 332.77 p/MPa

F/kg‚m-3

1.019 2.029 3.030 4.019 5.026 6.037 7.035 8.021 9.012 10.008 11.026 12.020 13.012 14.016 15.015 16.015 17.020 18.020 19.022 20.017

1094.5 1095.3 1096.0 1096.7 1097.4 1098.1 1098.8 1099.5 1100.1 1100.8 1101.5 1102.2 1102.8 1103.4 1104.2 1104.7 1105.4 1106.1 1106.7 1107.3

T/K ) 342.63

T/K ) 352.41

p/MPa

F/kg‚m-3

p/MPa

F/kg‚m-3

1.018 2.039 3.009 4.022 5.025 5.925 7.031 8.009 9.007 10.024 11.013 12.012 13.000 14.019 15.027 16.019 17.009 18.015 19.019 20.018

1085.6 1086.3 1087.0 1087.8 1088.5 1089.1 1089.9 1090.6 1091.3 1092.0 1092.7 1093.4 1094.1 1094.8 1095.4 1096.1 1096.8 1097.5 1098.2 1098.8

1.015 2.020 3.016 4.038 5.000 6.001 7.017 8.008 9.017 10.026 11.018 12.014 13.014 14.022 15.028 16.020 17.023 18.015 19.016 20.019

1076.7 1077.4 1078.1 1078.8 1079.5 1080.4 1081.1 1082.0 1082.6 1083.4 1084.1 1084.7 1085.4 1086.2 1086.8 1087.6 1088.2 1088.8 1089.5 1090.2

Table 3. Experimental Densities G of the Hexane (1) + Benzothiophene (2) Mixture at x1 ) 0.2588 T/K ) 312.99

T/K ) 322.89

T/K ) 332.66

T/K ) 342.55

T/K ) 352.33

p/MPa

F/kg‚m-3

p/MPa

F/kg‚m-3

p/MPa

F/kg‚m-3

p/MPa

F/kg‚m-3

p/MPa

F/kg‚m-3

1.009 2.023 3.016 4.029 5.004 6.021 7.031 8.005 9.022 10.016 11.004 12.015 13.015 14.003 15.011 16.003 17.010 18.002 19.029 20.017

1009.0 1009.7 1010.5 1011.2 1011.9 1012.6 1013.3 1014.0 1014.8 1015.4 1016.1 1016.8 1017.5 1018.2 1018.9 1019.5 1020.2 1020.9 1021.5 1022.2

1.017 2.023 3.021 4.016 5.026 6.030 7.028 8.018 9.014 10.021 11.005 12.022 13.013 14.012 15.017 16.016 17.002 18.014 19.024 20.016

1000.0 1000.8 1001.5 1002.3 1003.1 1003.8 1004.6 1005.3 1006.0 1006.7 1007.5 1008.2 1008.9 1009.6 1010.3 1011.0 1011.7 1012.4 1013.1 1013.8

1.020 2.021 3.022 4.018 5.021 6.012 7.018 8.005 9.012 10.011 11.013 12.006 13.011 14.000 15.025 16.005 17.000 18.002 19.009 20.016

991.1 991.9 992.7 993.5 994.3 995.0 995.8 996.6 997.3 998.2 998.9 999.7 1000.4 1001.2 1002.0 1002.6 1003.3 1004.1 1004.8 1005.5

1.028 2.013 3.013 4.017 5.024 6.012 7.004 8.017 9.012 10.016 11.015 12.022 13.030 14.011 15.020 16.020 17.017 18.008 19.011 20.013

982.2 983.1 983.8 984.7 985.5 986.3 987.1 987.9 988.7 989.5 990.4 991.2 992.0 992.8 993.6 994.3 995.1 995.8 996.6 997.4

1.030 2.012 3.021 4.018 5.020 6.024 7.016 8.000 9.020 10.010 11.018 12.012 13.013 14.007 15.016 16.012 17.013 18.003 19.011 20.014

973.2 973.9 974.8 975.8 976.6 977.6 978.5 979.3 980.2 981.0 981.9 982.7 983.5 984.3 985.2 986.0 986.8 987.6 988.4 989.1

Differentiation of eq 2 and substituting the results in eqs 8 and 9 leads to

root-mean-square

RMS )

x∑ 1 n

n

(% ∆Vi)2

(7)

i)1

where % ∆Vi ) 100(Vexptl - Vcalcd )/Vexptl . n represents the i i i number of correlated data. The parameters and statistical values for hexane for eq 2 are presented in Table 7. Deviations between experimental and calculated densities with eq 2 are presented in Figure 1. As can be seen, densities of hexane are well represented for the equation in the studied range of pressures and temperatures. Almost all of the deviations showed in this figure are within the experimental uncertainty which is better than 0.035 %. DeriWed Properties. Isothermal compressibilities and isobaric thermal expansivities of hexane were calculated according to 1 ∂F F ∂p

( ) 1 ∂F R )- ( ) F ∂T κT )

p

T

p

(8) (9)

κT )

c2 1 1/3 c3 - (c4/T + c5/T ) + p c1 + c2p

Rp ) -

[

c4/T2 + c5/3T4/3

c3 - (c4/T + c5/T1/3) + p

]

(10)

(11)

The excess molar volume for a binary mixture is calculated with the expression VE )

(

)

Mmix x1M1 x2M2 + Fmix F1 F2

(12)

In this equation, the excess molar volume VE is calculated by using the density F, molecular weight M, and the mole fraction x. The subscripts 1 and 2 and mix denote hexane, benzothiophene, and the mixture, respectively. In the calculation of excess molar volumes of hexane (1) + benzothiophene (2) mixtures, Fmix was taken from Tables 2 to 6 and F1 and F2 were calculated with eq 2 using the parameters

2458



T/K ) 322.05

T/K ) 332.90

T/K ) 342.79

T/K ) 352.63

T/K ) 362.50

p/MPa

F/kg‚m-3

p/MPa

F/kg‚m-3

p/MPa

F/kg‚m-3

p/MPa

F/kg‚m-3

p/MPa

F/kg‚m-3

p/MPa

F/kg‚m-3

1.025 2.010 3.028 4.011 5.013 6.021 7.010 8.033 9.029 10.015 11.018 12.012 13.010 14.022 15.019 16.008 17.018 18.027 19.006 20.006

910.7 911.5 912.4 913.2 914.0 914.8 915.6 916.4 917.2 918.0 918.8 919.5 920.3 921.0 921.8 922.6 923.3 924.1 924.8 925.5

1.026 2.020 3.015 4.003 5.014 6.021 7.015 8.009 9.028 10.013 11.021 12.023 13.008 14.021 15.012 16.018 17.012 18.012 19.007 20.015

901.9 902.8 903.7 904.5 905.4 906.3 907.2 908.0 908.9 909.7 910.5 911.3 912.1 913.0 913.7 914.5 915.3 916.1 916.9 917.7

1.028 2.010 3.021 4.018 5.018 6.008 7.019 8.016 9.023 10.018 11.007 12.010 13.019 14.015 15.019 16.002 17.014 18.017 19.023 20.028

892.5 893.2 894.1 895.3 896.2 897.0 897.9 898.8 899.8 900.7 901.6 902.4 903.3 904.2 905.0 905.9 906.7 907.5 908.3 909.1

1.022 2.032 3.024 4.029 5.019 6.019 7.035 8.022 9.016 10.010 11.010 12.024 13.001 14.017 15.021 16.020 17.009 18.009 19.011 20.011

883.3 884.3 885.3 886.4 887.3 888.3 889.3 890.2 891.1 892.0 893.0 893.9 894.8 895.7 896.6 897.4 898.3 899.2 900.0 900.9

1.037 2.029 3.026 4.032 5.015 6.024 7.028 8.017 9.003 10.022 11.024 12.013 13.038 14.000 15.021 16.012 17.010 18.015 19.022 20.005

874.2 875.3 876.4 877.5 878.5 879.5 880.5 881.5 882.5 883.5 884.5 885.4 886.4 887.3 888.2 889.1 890.0 890.9 891.8 892.7

1.028 2.025 3.020 4.000 5.045 6.017 7.018 8.013 9.024 10.011 11.008 12.025 13.004 14.014 15.011 16.027 17.017 18.030 19.022 20.002

864.8 866.0 867.1 868.2 869.3 870.4 871.5 872.5 873.6 874.6 875.6 876.6 877.6 878.6 879.6 880.6 881.5 882.5 883.4 884.3


T/K ) 323.02

T/K ) 332.86

T/K ) 342.72

T/K ) 352.53

T/K ) 362.33

p/MPa

F/kg‚m-3

p/MPa

F/kg‚m-3

p/MPa

F/kg‚m-3

p/MPa

F/kg‚m-3

p/MPa

F/kg‚m-3

p/MPa

F/kg‚m-3

1.017 2.027 2.000 3.031 4.039 5.021 6.027 7.021 8.054 9.007 10.018 11.018 12.036 13.021 14.007 15.006 16.012 17.016 18.000 19.017 20.030

761.8 762.9 735.8 764.0 764.9 765.9 766.9 767.9 768.9 769.8 770.7 771.6 772.6 773.5 774.3 775.2 776.0 776.9 777.8 778.6 779.5

1.017 2.013 2.026 3.014 4.012 5.008 6.010 7.025 8.028 9.009 10.010 11.002 12.017 13.019 14.006 15.015 16.022 17.019 18.016 19.024 20.021

752.7 753.8 726.5 754.9 756.0 757.1 758.1 759.2 760.2 761.2 762.2 763.2 764.1 765.1 766.0 767.0 767.9 768.8 769.8 770.6 771.5

1.031 2.024 2.034 3.019 4.001 5.002 6.020 7.005 8.013 9.004 10.000 11.019 12.006 13.014 14.008 15.007 16.009 17.002 18.026 19.007 20.017

743.7 744.9 716.8 746.1 747.2 748.4 749.5 750.6 751.7 752.8 753.8 754.9 755.9 757.0 757.9 758.9 759.9 760.9 761.8 762.8 763.7

1.034 2.000 3.023 4.016 5.014 6.014 7.019 8.012 9.010 10.013 11.016 12.016 13.011 14.001 15.003 16.025 17.012 18.018 19.008 20.017

734.5 735.8 737.0 738.2 739.5 740.7 741.8 743.0 744.1 745.3 746.4 747.5 748.6 749.6 750.7 751.7 752.8 753.8 754.7 755.8

1.026 2.026 3.024 4.034 5.014 6.040 7.028 8.017 9.003 10.008 11.016 12.002 13.020 14.016 15.037 16.035 17.020 18.020 19.008 20.019

725.1 726.5 727.8 729.2 730.5 731.8 733.0 734.3 735.5 736.7 737.9 739.0 740.2 741.3 742.5 743.6 744.6 745.7 746.7 747.8

1.020 2.034 3.013 4.007 5.015 6.018 7.015 8.017 9.024 10.010 10.996 12.027 13.022 14.016 15.023 16.012 17.011 18.012 19.030 20.017

715.3 716.8 718.3 719.7 721.2 722.5 723.9 725.2 726.5 727.8 729.1 730.4 731.6 732.8 734.0 735.1 736.3 737.4 738.6 739.7

obtained in this work for hexane and those reported by JimeńezGallegos15 for benzothiophene (see Table 7) to have the same values of temperature and pressure for all mixtures. A typical behavior for the excess molar volumes of the studied mixtures can be observed in Figures 2 and 3. The uncertainty for calculated excess molar volumes in this work is estimated within 0.065 cm3‚mol-1.

Results and Discussion Experimental densities of hexane in this work were correlated with the five-parameter MTS and compared with those from the literature7-9 and those calculated with the equation of state proposed by Span and Wagner.16 A detailed procedure for calculation of densities with this equation is given in ref 16. Deviations between experimental and calculated densities of hexane are plotted in Figure 4. Good agreement is observed. Deviations were within -0.13 % and +0.04 %. Densities of hexane were also compared with those calculated with the Tait equation using parameters reported by Cibulka17 and Cibulka and Hnedkovsky´18

[

F ) Fref 1 - CT ln

BT + p BT + pref

]

-1

(13)

where Fref is the reference density computed as NA

Fref ) FC[1 +

∑a

Ti(1

- T/TC)(i/3)]

(14)

i)1

aT are the adjusted parameters of the equation for a pure compound; NA is the maximum number of parameters; FC is the critical density; T is the system temperature; and TC is the critical temperature of the substance. The values of BT and CT of eq 13 were calculated from NB

BT )

∑b

Ti[(T

- T0)/100]i

(15)

Ti[(T

- T0)/100]i

(16)

i)0 NC

CT )

∑c i)0

where bT and cT are the group of parameters reported by Cibulka and Hnedkovsky´18 and NB and NC are the number of parameters. T0 is a fixed temperature for hexane. pref is the reference pressure in eq 13 and is equal to 0.101325 MPa when the measurement temperature is under the normal boiling point of hexane;

Journal of Chemical and Engineering Data, Vol. 52, No. 6, 2007 2459 Table 6. Experimental Densities G of the Hexane (1) + Benzothiophene (2) Mixture at x1 ) 0.9432 T/K ) 313.11 p/MPa

F/kg‚m-3

1.023 2.023 3.037 4.019 5.025 6.058 7.008 8.047 9.025 10.040 11.000 12.016 13.019 14.016 15.029 16.024 17.011 18.015 19.046 20.016

669.0 670.0 671.0 672.2 673.3 674.4 675.5 676.6 677.6 678.6 679.6 680.7 681.6 682.6 683.6 684.5 685.5 686.4 687.4 688.2

T/K ) 323.09 p/MPa

F/kg‚m-3

1.017 2.024 3.024 4.016 5.024 6.021 7.018 8.020 9.019 10.010 11.012 12.013 13.021 14.023 15.015 16.001 17.028 18.003 19.001 20.017

659.3 660.6 661.9 663.1 664.2 665.5 666.6 667.8 668.9 670.0 671.1 672.2 673.3 674.3 675.3 676.3 677.3 678.3 679.3 680.3

T/K ) 332.82 p/MPa

F/kg‚m-3

1.026 2.016 3.016 4.023 5.004 6.016 7.012 8.018 9.014 10.014 11.009 12.005 13.020 14.007 15.005 16.012 17.015 18.010 19.000 20.001

650.1 651.4 652.8 654.1 655.4 656.7 658.0 659.2 660.5 661.6 662.8 664.0 665.1 666.3 667.3 668.4 669.5 670.6 671.6 672.6

otherwise, pref is the vapor pressure of hexane calculated with the equation

T/K ) 342.71 p/MPa

F/kg‚m-3

1.025 2.014 3.011 4.027 5.014 6.027 7.019 8.015 9.010 10.003 11.017 12.006 13.024 14.021 15.006 16.015 17.016 18.000 19.034 20.012

640.4 641.8 643.3 644.8 646.2 647.6 649.0 650.3 651.6 652.9 654.2 655.4 656.7 657.8 659.0 660.2 661.3 662.4 663.6 664.6

T/K ) 352.53 p/MPa

p/MPa

F/kg‚m-3

1.025 2.023 3.030 4.018 5.021 6.018 7.010 8.018 9.044 10.011 11.022 12.013 13.005 14.000 15.021 16.022 17.001 18.013 19.007 20.039

630.4 632.1 633.8 635.4 637.0 638.5 639.9 641.4 642.8 644.2 645.5 646.9 648.2 649.5 650.8 652.0 653.2 654.4 655.6 656.7

1.028 2.031 3.031 4.012 5.026 6.013 7.022 8.014 9.000 10.011 11.007 12.007 13.008 14.024 15.002 16.016 17.000 18.008 19.018 20.028

620.3 622.2 624.0 625.7 627.4 629.1 630.7 632.3 633.7 635.3 636.7 638.2 639.6 640.9 642.3 643.6 644.9 646.3 647.5 648.8

Table 7. Parameters of the Five-Parameter MTS Equation6 for Hexane and Benzothiophene benzothiophenea

hexane

log pref ) Avp - Bvp/(T + Cvp - 273.15)

(17)

where Avp ) 4.00139, Bvp ) 1170.875, and Cvp ) 224.317 were taken from ref 19. Deviations between data reported in this work and those calculated with eq 13 are plotted in Figure 4. Good agreement can be seen with deviations better than 0.05 %, but it is greater at 362.40 K for some data points. Nevertheless, deviations in this isotherm are within 0.10 %, so the agreement is still good. Cibulka and Hnedkovsky´18 reported the statistical values for their correlation as RMSD ) 0.693 kg‚m-3, RMSDr ) 0.112 %, and bias ) -0.033 kg‚m-3. Following the same procedure, the statistics for this work are RMSD ) 0.200 kg‚m-3, RMSDr ) 0.032 %, and bias ) 0.060 kg‚m-3. Because temperatures and pressures in this work are not equal to the experimental data from the literature, the MTS equation was used for comparisons. Figure 5 shows the differences between densities of hexane calculated by using eq 2 and literature data. The deviations were slightly greater than those plotted in Figure 4.

Figure 1. Deviations between experimental densities Fexptl of hexane with those calculated with eq 2, Fcalcd, at: B, 313.12 K; O, 323.05 K; 1, 332.85 K; 4, 342.73 K; 9, 352.56 K; and 0, 362.40 K.

T/K ) 362.31

F/kg‚m-3

/MPa‚kg-1‚m3

c1 c2/kg-1‚m3 c3/MPa c4/K‚MPa c5/K1/3‚MPa AAD/% bias/% SDV/% RMS/% Tmin /K Tmax /K pmin /MPa pmax /MPa n a

0.1104 1.3290‚10-3 -248.93 34929.44 -2928.28 1.63‚10-2 -4.94‚10-5 2.05‚10-2 2.04‚10-2 313.12 362.40 1.010 25.030 150

c1/MPa‚kg-1‚m3 c2/kg-1‚m3 c3/MPa c4/K‚MPa c5/K1/3‚MPa AAD/% bias/% SDV/% RMS/% Tmin /K Tmax /K pmin /MPa pmax /MPa n

0.2442 7.3852‚10-4 -2.6262 9819.83 -2129.88 7.33‚10-3 1.53‚10-4 8.68‚10-3 8.64‚10-3 314.04 352.80 1.010 20.020 100

From ref 15.

Calculated isothermal compressibilities of hexane from eq 10 (κcalcd ) were compared with those reported by Daridon et T al.20 and Pecˇar and Dolecˇek21 (κlit T ). In Figure 6, residuals between values reported in the literature and those calculated

Figure 2. Excess molar volumes VE calculated with the five-parameter equation MTS at ∼353 K for the hexane + benzothiophene mixtures: O, 1 MPa; 3, 5 MPa; 0, 10 MPa; ], 15 MPa; and 4, 20 MPa. Solid lines denote a trend.

2460


Figure 3. Excess molar volumes VE calculated with the five-parameter equation MTS at ∼20 MPa for the hexane + benzothiophene mixtures: O, 313 K; 3, 323 K; 0, 333 K; ], 343 K; and 4, 353 K. Solid lines denote a trend.

Figure 6. Residuals for the isothermal compressibilities of hexane κcalcd T calculated with the five-parameter equation and those taken from the lit 20 literature, κT . Daridon et al.: B, 313.15 K; 1, 323.15 K; 9, 333.15 K; [, 343.15 K; 2, 353.15 K; and \, 363.15 K. Pecˇar and Dolecˇek:21 O, 323.15 K; and 3, 348.15 K. Table 8. Residuals between Isobaric Thermal Expansivities Rlit p of , Calculated Hexane Reported in Ref 21 and Those Values, Rcalcd p with Equation 2 T/K ) 323.15

T/K ) 348.15

p/MPa

calcd )/103‚K-1 (Rlit p - Rp

p/MPa

calcd (Rlit )/103‚K-1 p - Rp

10.00 20.00

-0.158 -0.286

10.00 20.00

-0.179 -0.348

There is little data to compare with calculated values for the isobaric thermal expansivities in the correlated range of temperatures and pressures of this work. Table 8 shows residuals between the isobaric thermal expansivities reported by Pecˇar and Dolecˇek.21

Conclusions Fexptl

Figure 4. Deviations between experimental densities of hexane with those calculated Fcalcd with the Span and Wagner equation of state16 (open symbols) and with the Tait equation17,18 (solid symbols) at: B, 313.12 K; 1, 323.05 K; 9, 332.85 K; [, 342.73 K; 2, 352.56 K; and \, 362.40 K.

Densities of hexane and hexane + benzothiophene mixtures were obtained by means of a vibrating tube densimeter in the temperature range of (313 to 363) K and in the pressure range of (1 to 20) MPa. Densities for hexane + benzothiophene mixtures have not been reported previously. The hexane densities were compared with experimental data from the literature and with densities calculated with the equation of state of Span and Wagner16 and the Tait equation with parameters taken from Cibulka and Hnedkovsky´.18 Good agreement was observed in all cases. The modified Toscani-Szwarc equation6 yields good representation of densities, isothermal compressibilities, and isobaric thermal expansivities for hexane.

Literature Cited

Figure 5. Deviations between experimental densities of hexane reported in the literature Fexptl with those calculated Fcalcd with eq 2. Sauermann et al.7 at: B, 313.15 K; 1, 333.15 K; 9, 353.15 K. Stewart et al.8 at: [, 310.92 K; ], 344.24 K. Troncoso et al.9 at: O, 313.15 K.

with eq 10 are plotted. Good agreement was observed for this property.

(1) Elizalde-Solis, O.; Galicia-Luna, L. A. High pressure vapor-liquid equilibria for the systems thiophene + nonane + CO2, and thiophene + decane + CO2. Fluid Phase Equilib. 2005, 236, 178-183. (2) Serrano-Cocoletzi, V.; Galicia-Luna, L. A.; Elizalde-Solis, O. Experimental determination of the solubility of thiophene in carbon dioxide and in carbon dioxide + ethanol. J. Chem. Eng. Data 2005, 50, 16311634. (3) Elizalde-Solis, O.; Galicia-Luna, L. A. Solubility of thiophene + pentane and thiophene + octane binary mixtures in supercritical carbon dioxide at temperatures from 333 to 383 K. Ind. Eng. Chem. Res. 2005, 44, 5757-5760. (4) Zuń˜iga-Moreno, A; Galicia-Luna, L. A.; Betancourt-Ca´rdenas, F. F. Compressed liquid densities and excess volumes of CO2 + thiophene binary mixtures from 313 to 363 K and pressures up to 25 MPa. Fluid Phase Equilib. 2005, 236, 193-204. (5) Zuń˜iga-Moreno, A.; Galicia-Luna, L. A.; Camacho-Camacho, L. E. Measurements of solid solubilities and volumetric properties of

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(6)

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(10)

(11) (12) (13) (14)

naphthalene + carbon dioxide mixtures with a new assembly taking advantage of a vibrating tube densitometer. Fluid Phase Equilib. 2005, 234, 151-163. Zuń˜iga-Moreno, A.; Galicia-Luna, L. A.; Camacho-Camacho, L. E. Compressed liquid densities and excess volumes of CO2 + decane mixtures from (313 to 363) K and pressures up to 25 MPa. J. Chem. Eng. Data 2005, 50, 1030-1037. Sauermann, P.; Holzapfel, K.; Oprzynski, J.; Kohler, F.; Poot, W.; de Loos, T. W. The pFT properties of ethanol + hexane. Fluid Phase Equilib. 1995, 112, 249-272. Stewart, D. E.; Sage, B. W.; Lacey, W. N. Volumetric behavior of n-hexane in liquid phase. Ind. Eng. Chem. 1954, 46, 2529-2531. Troncoso, J.; Bessie`res, D.; Cerdeirinã, C. A.; Carballo, E.; Romanı´, L. Automated measuring device of (p, F, T) data. Application to the 1-hexanol + n-hexane system. Fluid Phase Equilib. 2003, 208, 141154. Galicia-Luna, L. A.; Richon, D.; Renon, H. New loading technique for a vibrating tube densimeter and measurements of liquid densities up to 39.5 MPa for binary and ternary mixtures of the carbon dioxidemethanol-propane system. J. Chem. Eng. Data 1994, 39, 424-431. Wagner, W.; Pruss, A. The IAPWS formulation 1995 for the thermodynamic properties of ordinary water substance for general and scientific. J. Phys. Chem. Ref. Data 2002, 31, 387-535. Span, R.; Lemmon, E. W.; Jacobsen, R. T.; Wagner, W. A Reference Quality Equation of State for Nitrogen. Int. J. Thermophys. 1998, 19, 1121-1132. Press, W. H.; Teukolsky, S. A.; Vetterling, W. T.; Flannery, B. P. Numerical Recipes in Fortran 77, 2nd ed.; Cambridge, MA, 1999; pp 678-683. Jacobsen, R. T.; Penoncello, S. G.; Lemmon, E. W.; Span, R. Multiparameter Equations of State. In Equations of State for Fluids

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Received for review July 10, 2007. Accepted September 3, 2007. The authors thank CONACYT and IPN for their financial support.

JE7003929

Experimental Densities of Hexane+ Benzothiophene Mixtures from

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